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Published at December 4

A Novel and Simple Invariant-Domain-Preserving Framework for PAMPA Scheme: 1D Case

math.NA

cs.NA

physics.comp-ph

physics.flu-dyn

Released Date: December 4, 2024

Authors: Rémi Abgrall, Miaosen Jiao¹, Yongle Liu², Kailiang Wu³

Aff.: ¹Department of Mathematics, Southern University of Science and Technology; ²Institute of Mathematics, University of Zürich; ³Department of Mathematics and Shenzhen International Center for Mathematics, Southern University of Science and Technology

Arxiv: http://arxiv.org/pdf/2412.03423v1

	IDP PAMPA		IDP PAMPA with OE		IDP PAMPA with MP
$N$	Error	Order	Error	Order	Error	Order
20	2.66e-2	-	4.12e-2	-	2.68e-2	-
40	5.60e-3	2.25	6.60e-3	2.63	5.40e-3	2.30
80	8.62e-4	2.69	8.76e-4	2.92	8.57e-4	2.67
160	1.09e-4	2.98	1.09-4	3.00	1.09e-4	2.97
320	1.37e-5	3.00	1.37e-5	3.00	1.37e-5	3.00
640	1.71e-6	3.00	1.71e-6	3.00	1.71e-6	3.00
1280	2.14e-7	3.00	2.14e-7	3.00	2.14e-7	3.00
20	2.94e-2	-	4.34e-2	-	2.93e-2	-
40	5.50e-3	2.42	6.50e-3	2.73	5.30e-3	2.47
80	8.49e-4	2.69	8.73e-4	2.90	8.39e-4	2.65
160	1.09e-4	2.96	1.09e-4	3.00	1.09e-4	2.95
320	1.36e-5	3.00	1.36e-5	3.00	1.36e-5	3.00
640	1.71e-6	3.00	1.71e-6	3.00	1.71e-6	3.00
1280	2.14e-7	3.00	2.14e-7	3.00	2.14e-7	3.00